At present, little theoretical results are obtained in affiliation network models although
many properties of statistical models for one-mode networks are derived [e.g., [1]}, [2]}, [3]}].
Even in the aforementioned simple [4]}'s model by assuming
that all edges are independent,
the asymptotic properties of the maximum likelihood estimator (MLE) are still not addressed due to a growing dimension of parameter space.
In this paper, we study the asymptotic properties of the MLE in
an affiliation model with the degree sequence as the exclusively natural sufficient statistic
in the exponential family distributions.
This model is identical to the [4]} model for unweighed edges (i.e., binary edges).
We establish the uniform consistency and asymptotic normality of the maximum likelihood estimator when the
number of actors and events both go to infinity. A key step to the proof is that we make use of
the approximate inverse of the Fisher information matrix with small approximation errors,
which is the extension of that used in [6]}.
